Given:
The capacity of the gas tank = 16 gallon
He filled the gas tank and used half of it for a trip i.e
fraction of gallon used = 1/2
Solution
The gallon of gas used can be calculated using the formula:
[tex]\text{gallon of gas used = fraction of gallon used }\times\text{ gallon of gas filled}[/tex]Substituting, we have:
[tex]\begin{gathered} \text{gallon of gas used = }\frac{1}{2}\text{ }\times\text{ 16} \\ =\text{ 8 gallons} \end{gathered}[/tex]Answer: 8 gallo
From the diagram below, we can tell that Δ ABC is similar to ____.
From the diagram, we get that
[tex]\measuredangle ABD\cong\measuredangle ADB.[/tex]By the reflexive property of congruence, we know that:
[tex]\measuredangle A\cong\measuredangle A.[/tex]Therefore, by the Angle-Angle criterion:
[tex]\Delta ABC\sim\Delta ADB.[/tex]Answer: [tex]\Delta ADB.[/tex]Given f(x)=2x-1 and g(x) =x^2 -2A) f(5)B) f(g(3))C) f(a+1) - f(a)D) g(2f(-1))E) g(x+h) -g(x)/h
2x + h
Explanation:
Given the following functions
f(x) = 2x - 1
g(x) = x^2 - 2
We are to simplify the expressionn:
[tex]\frac{g(x+h)-g(x)}{h}[/tex]Substitute the given functions into the expression and simplify
[tex]\begin{gathered} \frac{\lbrack(x+h)^2-2\rbrack-(x^2-2)}{h} \\ \frac{\lbrack\cancel{x^2}^{}+2xh+h^2-\cancel{2}-\cancel{x^2}^{}+\cancel{2}}{h} \\ \frac{2xh+h^2}{h} \end{gathered}[/tex]Factor out "h" from the numerator to have:
[tex]\begin{gathered} \frac{\cancel{h}(2x+h)}{\cancel{h}} \\ 2x+h \end{gathered}[/tex]Hence the simplified form of the expression is 2x + h
How to find the diagonal side one triangle like the measure with the Pythagorean Theorem
How to find the diagonal side one triangle like the measure with the Pythagorean Theorem
see the attached figure to better understand the p
Tickets to a play cost $10 at the door and $8 in advance.
The theatre club wants to raise at least $800 from the sale of the tickets from the play. Write and
graph an inequality for the number of tickets the theatre club needs to sell. If
the club sells 40 tickets in advance, how many does it need to sell at the door to
reach its goal? Use x to represent the number of tickets sold at the door. Use y
to represent the number of tickets sold in advance.
The system of linear inequality is solved to determine that they need to sell at least 48 door ticket. The graph of the problem is attached below
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
To solve this problem, we have to write out a system of linear inequality and solve.
x = number of tickets sold at doory = number of tickets sold in advance10x + 8y ≥ 800 ...eq(i)
y = 40 ...eq(ii)
put y = 40 in eq(i)
10x + 8(40) ≥ 800
10x + 320 ≥ 800
10x ≥ 800 - 320
10x ≥480
x ≥ 48
They need to sell at least 48 door tickets to meet the target.
The graph of the inequality is attached below
Learn more on system of linear inequality here
https://brainly.com/question/23093488
#SPJ1
A new cell phone costs $108.99 in the store. What would your total cost be if the sale tax is 7.5% ? Round your answer to the nearest cent, if necessary.
to calculate the tax we need to multiply the % by the price of the cellphone
7.5%=0.075
108.99*0.075=8.17
and the total cost is:
$108.99 + $8.17= 117.16
So the answer is: $
turn the expression from radical form to exponential expression in fractional form. No need to evaluate just be out in simplest form
To answer this question, we need to remember the next property of radicals:
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]In this case, we have that:
[tex]\sqrt[3x]{5}[/tex]And we can see that the exponent for 5 is m = 1. Therefore, we can rewrite the expression as follows:
[tex]\begin{gathered} \sqrt[3x]{5}=5^{\frac{1}{3x}} \\ \end{gathered}[/tex]In summary, therefore, we can say that the radical form to an exponential in fractional form is:
[tex]undefined[/tex]I will give brainliest if you help me with this problem not joking
Answer: 9+6+-6+-7
Step-by-step explanation:
im not sure thats my guess tho
4. Find the midpoint of DK, given the coordinates D (-10, -4) and K is located at the origin.m:|| m:1 m:Midpoint:Equation of the line:
The midpoint between two coordinates can be calculated using the equation
[tex]m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Point D has the coordinates (-10, -4). The problem stated that point K is located at the origin, hence, we can say that its coordinates are (0, 0).
Using the formula stated above to solve the coordinates of the midpoint, we get
[tex]\begin{gathered} m=(\frac{-10+0}{2},\frac{-4+0}{2}) \\ m=(\frac{-10}{2},-\frac{4}{2}) \\ m=(-5,-2) \end{gathered}[/tex]Answer: The midpoint of the line segment DK is located at (-5,-2).
If the two expressions are equivalent, find value of x
1. Subtract 1/x in both sides of the equation:
[tex]\begin{gathered} \frac{5}{x}-\frac{1}{x}-\frac{1}{3}=\frac{1}{x}-\frac{1}{x} \\ \\ \frac{4}{x}-\frac{1}{3}=0 \end{gathered}[/tex]2. Add 1/3 in both sides of the equation:
[tex]\begin{gathered} \frac{4}{x}-\frac{1}{3}+\frac{1}{3}=0+\frac{1}{3} \\ \\ \frac{4}{x}=\frac{1}{3} \end{gathered}[/tex]3. Multiply both sides of the equation by x:
[tex]\begin{gathered} x\cdot\frac{4}{x}=x\cdot\frac{1}{3} \\ \\ 4=\frac{x}{3} \end{gathered}[/tex]4. Multiply both sides of the equation by 3:
[tex]\begin{gathered} 4\cdot3=\frac{x}{3}\cdot3 \\ \\ 12=x \\ \\ \text{ Rewrite} \\ x=12 \end{gathered}[/tex]Then, the value of x is 12Solve the following system of linear equations by graphing:4.Ex+3y54 9- 5858615+cilo=Answer 2 PointsKeypadKeyboard ShortcutsGraph the linear equations by writing the equations in slope-intercept form:y =Ixty =IxtIdentify the appropriate number of solutions. If there is a solution, give thepoint:O One SolutionO No SolutionO Infinite Number of Solutions
We have a system of equations:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \end{gathered}[/tex]We have to write the equations in slope-intercept form.
We start with the first equation:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ 3y=-\frac{58}{5}+\frac{4}{5}x \\ 5\cdot3y=4x-58 \\ 15y=4x-58 \\ y=\frac{4}{15}x-\frac{58}{15} \end{gathered}[/tex]For the second equation we get:
[tex]\begin{gathered} \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \\ \frac{9}{5}y=\frac{86}{15}-\frac{4}{3}x \\ y=\frac{5}{9}\cdot\frac{86}{15}-\frac{5}{9}\cdot\frac{4}{3}x \\ y=\frac{86}{9\cdot3}-\frac{20}{27}x \\ y=-\frac{20}{27}x+\frac{86}{27} \end{gathered}[/tex]To graph the equations we need two points. We can easily identify the y-intercept from the equations, but we have to identify one more point for each equation.
We can give a value to x and find the corresponding value of y.
Then, for example we can calculate y for x = 1 in the first equation:
[tex]\begin{gathered} y=\frac{4}{15}(1)-\frac{58}{15} \\ y=\frac{4}{15}-\frac{58}{15} \\ y=-\frac{54}{15} \end{gathered}[/tex]Then, for the first equation we know the points (0, -58/15) and (1, -54/15).
For the second equation we can do the same, by giving a value of 1 to x (NOTE: we can give any arbitrary value to x, it does not have to be the same for both equations) and calculate y:
[tex]\begin{gathered} y=-\frac{20}{27}(1)+\frac{86}{27} \\ y=-\frac{20}{27}+\frac{86}{27} \\ y=\frac{66}{27} \end{gathered}[/tex]Now we know the points of the second equation: (0, 86/27) and (1, 66/27).
With such fractions we can not make an accurate graph in paper, as they don't match the divisions of the grid.
We can use approximate decimals values for the fractions and graph the points.
The approximations for the first equation are:
[tex]\begin{gathered} (0,-\frac{58}{15})\approx(0,-3.9) \\ (1,-\frac{54}{15})=(1,-3.6) \end{gathered}[/tex]and for the second equation:
[tex]\begin{gathered} (0,\frac{86}{27})\approx(0,3.2) \\ (1,\frac{66}{27})\approx(1,2.4) \end{gathered}[/tex]We can then graph the equations as:
If we graph the equations with the exact points, we get an intersection point at (7,-2).
This intersection is the unique solution to both equations at the same time, so it is the only solution to the system of equations.
Answer:
The equations in slope-intercept form are:
y = 4/15 x + (-58/15)
y = -20/27 * x + 86/27
The system has only one solution: (7, -2).
⦁ It takes the earth 24 h to complete a full rotation. It takes Mercury approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.
Answer:
Answer:
58 days, 15 h, and 30 min
Step-by-step explanation:
How do I find the restrictions on x if there are any? [tex] \frac{1}{x - 1} = \frac{5}{x - 10} [/tex]
We have the expression:
[tex]\frac{1}{x - 1}=\frac{5}{x - 10}[/tex]When we have rational functions, where the denominator is a function of x, we have a restriction for the domain for any value of x that makes the denominator equal to 0.
That is because if the denominator is 0, then we have a function f(x) that is a division by zero and is undefined.
If we have a value that makes f(x) to be undefined, then this value of x does not belong to the domain of f(x).
Expression:
[tex]\begin{gathered} \frac{1}{x-1}=\frac{5}{x-10} \\ \frac{x-1}{1}=\frac{x-10}{5} \\ x-1=\frac{x}{5}-\frac{10}{5} \\ x-1=\frac{1}{5}x-2 \\ x-\frac{1}{5}x=-2+1 \\ \frac{4}{5}x=-1 \\ x=-1\cdot\frac{5}{4} \\ x=-\frac{5}{4} \end{gathered}[/tex]Answer: There is no restriction for x in the expression.
using the rule of s-14 - (-2) = -12
We will have:
[tex]-14-(-2)=-12\Rightarrow-14+2=-12\Rightarrow-12=-12[/tex]Section 5.2-12. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).3x-3y = -6-x+2y = 8
the Given the simultaneous equations
[tex]\begin{gathered} 3x-3y=-6\text{ ------(1)} \\ -x+2y=8\text{ -------(2)} \end{gathered}[/tex]Solving the above equations by substitution method:
Step 1:
From equation 2, make x the subject of the formula
[tex]\begin{gathered} -x+2y=8 \\ \text{making x the subject of formula, we have} \\ x=2y-8\text{ -------(3)} \end{gathered}[/tex]Step 2:
Substitute equation 3 into equation 1
[tex]\begin{gathered} \text{From equation,} \\ 3x-3y=-6 \\ \text{Thus, we have} \\ 3(2y-8)-3y=-6 \\ \text{opening the brackets, we have} \\ 6y-24-3y=-6 \\ \text{collecting like terms, we have} \\ 6y-3y=-6+24 \\ 3y=18 \\ \text{divide both sides by the coefficient of y.} \\ \text{The coefficient of y is 3. Thus,} \\ y=\frac{18}{3}=6 \end{gathered}[/tex]Step 3:
Substitute the value of y in either equation 1 or 2.
[tex]\begin{gathered} \text{From equation 2,} \\ -x+2y=8 \\ \text{Thus,} \\ -x+2(6)=8 \\ -x+12=8 \\ \text{collecting like terms, we have} \\ -x=8-12 \\ -x=-4 \\ x=4 \end{gathered}[/tex]Thus, the values of (x, y) are (4, 6)
A circular arc has measure of 4 cm and is intercepted by a central angle of 73°. Find the radius r of the circle. Do not round any intermediate computations, and round your answer to the nearest tenth.r= __ cm
The arc lenghr is given by:
[tex]s=r\theta[/tex]where s is the arc lenght, r is tha raidus and theta is the angle measure in radians. Since in our problem the angle is given in degrees we have to convert it to radians, to do this we have to multiply the angle by the factor:
[tex]\frac{\pi}{180}[/tex]Then:
[tex]\theta=(73)(\frac{\pi}{180})[/tex]Plugging the value of the arc lenght and the angle in the first formula, and solving for r we have:
[tex]\begin{gathered} 4=r(73)(\frac{\pi}{180}) \\ r=\frac{4\cdot180}{73\cdot\pi} \\ r=3.1 \end{gathered}[/tex]Therefore, the radius of the circle is 3.1 cm.
In △GHI, m∠G = (9x - 2), m∠H = (3x - 19), and m∠I = (3x + 6)". Find m∠G.
Answer:
m∠G = 115 degrees
Explanation:
The sum of the angles in a triangle is 180 degrees.
In triangle GHI:
[tex]\begin{gathered} m\angle G+m\angle H+m\angle I=180\degree \\ \implies9x-2+3x-19+3x+6=180\degree \end{gathered}[/tex]First, solve for x:
[tex]\begin{gathered} 9x+3x+3x-2-19+6=180\degree \\ 15x-15=180\degree \\ 15x=180+15 \\ 15x=195 \\ x=\frac{195}{15} \\ x=13 \end{gathered}[/tex]Therefore, the measure of angle G is:
[tex]\begin{gathered} m\angle G=9x-2 \\ =9(13)-2 \\ =117-2 \\ m\angle G=115\degree \end{gathered}[/tex]The measure of angle G is 115 degrees.
help me please asap!!!
The slope of the function is 1/2 and the y - intercept is 2
The standard form of slope-intercept form of line is y = mx + b
where , m is slope of line
and b is y-intercept.
Observing the graph ,
we can say Linear function also passes through two points
At (4,0) on x-axis and at (0,2) on y-axis and
also , the graph is making right angles triangle at (0,0)
Slope of the function = m = Tan∅
Tan∅ = Perpendicular of right triangle / base of triangle
Perpendicular of triangle = 2 unit
and base = 4 unit
Tan∅ = 2/4 = 1/2
Therefore , slope of line = 1/2
equation of line : y = 1/2 x + b
This line is passing through (0,2)
2 = 1/2(0) + b
b = 2
Therefore , the y-intercept = 2
Hence , the equation of line = y = 1/2 x + 2
To know more about Slope of the line here ,
https://brainly.com/question/14511992
#SPJ1
I’m stuck on how to verify number 7 and how to find the possible value for sin theta
Given:
There are given the trigonometric function:
[tex]sec^2\theta cos2\theta=1-tan^2\theta[/tex]Explanation:
To verify the above trigonometric function, we need to solve the left side of the equation.
So,
From the left side of the given equation:
[tex]sec^2\theta cos2\theta[/tex]Now,
From the formula of cos function:
[tex]cos2\theta=cos^2\theta-sin^2\theta[/tex]Then,
Use the above formula on the above-left side of the equation:
[tex]sec^2\theta cos2\theta=sec^2\theta(cos^2\theta-sin^2\theta)[/tex]Now,
From the formula of sec function:
[tex]sec^2\theta=\frac{1}{cos^2\theta}[/tex]Then,
Apply the above sec function into the above equation:
[tex]\begin{gathered} sec^2\theta cos2\theta=sec^2\theta(cos^2\theta-s\imaginaryI n^2\theta) \\ =\frac{1}{cos^2\theta}(cos^2\theta-s\mathrm{i}n^2\theta) \\ =\frac{(cos^2\theta-s\mathrm{i}n^2\theta)}{cos^2\theta} \end{gathered}[/tex]Then,
[tex]\frac{(cos^{2}\theta- s\mathrm{\imaginaryI}n^{2}\theta)}{cos^{2}\theta}=\frac{cos^2\theta}{cos^2\theta}-\frac{sin^2\theta}{cos^2\theta}[/tex]Then,
From the formula for tan function:
[tex]\frac{sin^2\theta}{cos^2\theta}=tan^2\theta[/tex]Then,
Apply the above formula into the given result:
So,
[tex]\begin{gathered} \frac{(cos^{2}\theta- s\mathrm{\imaginaryI}n^{2}\theta)}{cos^{2}\theta}=\frac{cos^{2}\theta}{cos^{2}\theta}-\frac{s\imaginaryI n^{2}\theta}{cos^{2}\theta} \\ =1-\frac{s\mathrm{i}n^2\theta}{cos^2\theta} \\ =1-tan^2\theta \end{gathered}[/tex]Final answer:
Hence, the above trigonometric function has been proved.
[tex]sec^2\theta cos2\theta=1-tan^2\theta[/tex]Write the percent as decimal 49%
Solution;
Given: The given number in percentage is 49 %
Required: Decimal value of given percentage.
Explanation:
Convert percentage into decimal as follows:
[tex]49\text{ \%=}\frac{49}{100}[/tex][tex]49\text{ \%=0.49}[/tex]Therefore, the required answer is 0.49
Final answer: The de
2(3x + 8) = 6x + 16How many solutions does this equation have
Answer:
The equation has infinite number of solutions
Explanation:
Given the equation:
2(3x + 8) = 6x + 16
To know how many solutions this equation has, we need to solve it and see.
Remove the brackets on the left-hand side
6x + 16 = 6x + 16
The expression on the left-hand side is exactly the same as the one on the right-hand side, this reason, there is infinite number of solutions that would satisfy this.
The coordinates of the midpoint of GH are M(-2,5) and the coordinates of one endpoint are H(-3, 7).
The coordinates of the other endpoint are(
).
Echeck
? Help
< PREV - 1 2 3 4 5 6
-
NEXT >
What are the coordinates of the other endpoint
EXPLANATION :
From the problem, we have segment GH and the midpoint is M(-2, 5).
One of the endpoints has coordinates of H(-3, 7)
and we need to find the coordinates of G(x, y)
The midpoint formula is :
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) are the coordinates of G
(x2, y2) = (-3, 7) are the coordinates of H
and (-2, 5) are the coordinates of the midpoint.
Then :
[tex](-2,5)=(\frac{x+(-3)}{2},\frac{y+7}{2})[/tex]We can equate the x coordinate :
[tex]\begin{gathered} -2=\frac{x+(-3)}{2} \\ \\ \text{ cross multiply :} \\ -2(2)=x-3 \\ -4=x-3 \\ -4+3=x \\ -1=x \\ x=-1 \end{gathered}[/tex]then the y coordinate :
[tex]\begin{gathered} 5=\frac{y+7}{2} \\ \\ \text{ cross multiply :} \\ 5(2)=y+7 \\ 10=y+7 \\ 10-7=y \\ 3=y \\ y=3 \end{gathered}[/tex]Now we have the point (-1, 3)
ANSWER :
The coordinates of the other endpoint are G(-1, 3)
Evaluate the expression when x = 32 and y = 2.
x/14 A. 1/16
B.16/21
D.2
C.4
Answer:
I think its 16/21
Step-by-step explanation:
Answer:
2Step-by-step explanation:
Given x = 14, y = 2x/14
Void "y" because it is not in this equation.= x/14
32/14
= 2.2
≈ 2
Translate into proportion 16.4 is 45% of what number ?
Given:
16.4 is 45%
[tex]\begin{gathered} 16.4\times\frac{45}{100}=\frac{b}{1} \\ \frac{16.4}{b}=\frac{100}{45} \end{gathered}[/tex]Hence, the required option is D.
Multiple the binomials (simplify) (y-4)(y-8)
Given
[tex](y-4)(y-8)[/tex]Simplify as shown below
[tex]\begin{gathered} (y-4)(y-8)=y(y-8)-4(y-8)=y^2-8y-4y+(-4)(-8)=y^2-12y+32 \\ \Rightarrow(y-4)(y-8)=y^2-12y+32 \end{gathered}[/tex]The answer is y^2-12y+32
which of the following gives the line of symmetry
To be able to reflect the trapezoid to itself, the reflection must be at the point where the figure will be divided symmetrically.
For a trapezoid, it must be reflected at the center of its base.
In the given figure, the center of the base of the trapezoid falls at x = 4.
Thus, to reflect it by itself, it must be reflected at x = 4.
The answer is letter B.
Is this correct? If not can u show me how to do it
Given
[tex]k(x+y)=2x-4[/tex]Notice that it is the equation of a line.
Then, since it crosses (10,-2), set x=10 and y=-2 in the given equation, as shown below
[tex]\begin{gathered} x=10,y=-2 \\ \Rightarrow k(10-2)=2*10-4 \\ \Rightarrow k(8)=20-4 \\ \Rightarrow k=\frac{16}{8}=2 \\ \Rightarrow k=2 \end{gathered}[/tex]Thus, the answer is k=2.
the ratio of isabella's money to Shane's money is 5:10.if Isabelle has $55 how much money do Shane have?what about they have together?
A(0,3) B(1,6) C(4,6) D(5,3) rotate it around the origin 270 degrees clockwise
Please answer with the coordinates.
♥
The rule for a rotation by 270° about the origin is (x,y)→(y,−x)
so i guess A?
♥
Find the restricted values of x for the following rational expression. If there are no restricted values of x,indicate "No Restrictions".x² +8x² - x - 12AnswerHow to enter your answer (opens in new window)Separate multiple answers with commas.KeypadKeyboard ShortcutsSelecting a radio button will replace the entered answer value(s) with the radio button value. If the radiobutton is not selected, the entered answer is used.
Answer:
To find the restricted values of x for the given rational expression,
[tex]\frac{x^2+8}{x^2-x-12}[/tex]The above expression is defined only when x^2-x-12 not equal to 0.
x values are restricted for the solution of x^2-x-12=0
To find the values of x when x^2-x-12=0.
Consider, x^2-x-12=0
we get,
[tex]x^2-x-12=0[/tex][tex]x^2-4x+3x-12=0[/tex][tex]x\left(x-4\right)+3\left(x-4\right)=0[/tex]Taking x-4 as common we get,
[tex]\left(x-4\right)\left(x+3\right)=0[/tex]we get, x=4,x=-3
The restricted values of x are 4,-3.
we get,
[tex]x\ne4,-3[/tex]Answer is:
[tex]x\ne4,-3[/tex]Does the point (2, 6) satisfy the inequality 2x + 2y ≥ 16?
yes
no